Name:________________________________



Name:________________________________ Date:_______ Period:_____

Transformations Ms. Anderle

Transformations:

A transformation is an operation that maps an original geometric figure, a preimage, onto a new figure called the image. A transformation can change the _______________, ________________, or __________________ of an object.

A specific type of transformation is called an ___________________. This transformation preserves _________________________.

Types of Transformations:

1. Translation

• A translation ____________________ an object a fixed distance in any direction.

• The preimage and the image (translated figure) have the same __________ and ____________. They also ____________________.

Example:

• Mapping Rule:

Examples:

1. T5,3 A(2,3) 2. T-2,1B(4,-2) 3. T0,-5K(-2,-4)

4. T-3,4 G(x,y) 5. T5,4J(2k, k) 6. T-1,2T(2x, y)

7. If the image after T2,4 is (3,4) then what is the preimage?

8. If the image after T-2,-3 is (-2, -1) then what is the preimage?

9. If translation T maps point P(2,3) onto P’(-3,4), then find translation T.

10. If translation T maps point L(5,14) onto L’(-5,-2), then find translation T.

2. Line Reflections

• A line reflection is a transformation where an image is ________________ over a given line.

• Each point in the reflection is the ________________ from the line of reflection as the points in the original figure.

Example:

Line Reflection Mapping Rules

|Reflections in the x-axis | |

|Reflections in the y-axis | |

|Reflections in the y = x line | |

|Reflection in the y = -x line | |

|Reflection in the line y = k | |

|(where k is a constant) | |

|Reflection in the line x = k | |

|(where k is a constant) | |

1. Find the reflection in the y = -x line of ΔPQR with the coordinates P(2,2), Q(5,3), and R(3,-1).

2. Find the reflection of the figure whose coordinates are A(-1,3), B(4,6), C(7,2) across the line represented by x = 2.

3. Find the reflection of the figure whose coordinates are A(-3,-7), B(3,-4), and C(9,-6) across the line represented by y = -3.

4. State the coordinates of the point (-2,5) under the reflection

a. in the line y = x

b. in the line y = 4

c. in the line x = -2

5. Find the image of the points below in reflected in the line y = -2

a. (1, 4)

b. (-3, 3)

c. (4, -5)

3. Point Reflection and Symmetry

• If a figure is reflected in or through point P, then P is _______________ of the line segement joining each point to its corresponding image.

• Point Reflection Mapping Rules:

-Over the Origin

-Over a Given Point:

A figure is said to have point symmetry if the figure coincides with itself when reflected through a point or when rotated 180° about a point. The point that is the center of reflection or rotation is called the point of symmetry.

| |F, G, |

|Shapes without point symmetry | |

| |Z, S, N, |

|Shapes with point symmetry | |

Examples:

1. What letter has both point symmetry and line symmetry?

a. A b. H c. E d. S

2. What is the image of (k, 2k) after a reflection through the origin.

3. Find the image of (-4, 2) under the reflection in the point (2, 2).

4. Find the image of (-2, -6) under a point reflection in the origin.

5. Find the image of (3, 2) under the reflection in the point (-1, -1)

4. Rotations:

• A rotation is a transformation in which a figure is __________________ point called the __________________.

• In the coordinate plane, this point is typically the origin.

• Rotations that are counterclockwise are rotations of ____________________ degree measure.

• Rotations that are clockwise are of _________________ measure.

• All rotations are assumed to be clockwise about the origin unless otherwise stated

Example:

[pic]

Rotation Mapping Rules

|Rotation of 90° and -270° | |

|Rotation of 180° and -180° | |

|Rotation of 270° and -90° | |

|Rotation of 360° and -360° | |

Examples:

1. What is the image of (-2, 3) under a rotation of:

a) 90° b) 180° c) 270° d) -90° e) -270°

2. Name the coordinates of each point under a rotation of 90°

a) (5,1) b) (-3,3) c) (8, -2) d) (0,5)

3. Name the coordinates of each point under a rotation of 270°

a) (-3,2) b) (-2,-2) c) (4,4) d) (7,14)

5. Dilations

• A dilation is a transformation in which ___________ of a figure is changed and the figure is moved.

• Dilations are ______________________________________________.

Mapping Rule:

Model Problems:

1. D3(x, y) = (3x, 3y) 2. D1/2(2, 4) = (1, 2)

Note:

-If k = 1, then the image is identical to the original.

-If k = -1, then the image is congruent and is the same as a point reflection.

-If |k| > 1, then the image is similar and larger than the original.

-If |k| < 1, then the image is similar and smaller than the original.

Examples:

1) What are the coordinates of point (2, -4) under the dilation D-2?

2) What are the coordinates of point (9, -6) under the dilation D1/3?

3) What are the coordinates of point (12, -4) under the dilation D5?

4) If the dilation Dk(2, -4) = (-1, 2), the scale factor k is equal to:

5) Find the image of (6, -9) under the dilation D2/3.

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download